Questions

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 30 N? [NEET 2017]

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a

25 ms-2

b

0.25 rad s-2

c

25 rad s-2

d

5 ms-2

detailed solution

Correct option is C

Torque (τ) acting on a body and angular acceleration (α) produced in it are related asτ = IαConsider a hollow cylinder around which a rope is wounded.Torque acting on the cylinder due to the force F is τ=Fr.Now, we have τ = Iαwhere, I = moment of inertia of the cylinder about the axis through the centre.⇒ I=mr2Given, F=30N,m=3kg and r=40cm=40×10−2mAngular acceleration,α=τI=Frmr2=Fmr=303×40×10−2=1004=25rads−2

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